On the eulericity of a graph

Abstract

The eulericity ϵ(G) of a bridgeless graph G is defined as the least number of eulerian subgraphs of G which together cover the lines of G. A 1–1 correspondence is shown to exist between the k-tuples of eulerian subgraphs of G and the proper flows (mod2^k) on a given network based on G. The inequality ϵ(G) ⩽ 3 them follows from a result of Jaeger.